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Category Archives: Calculus
Maximizing with ratio of slant height to radius
A cone has radius r and fixed slant height of s cm. Find the ratio s:r which maximizes the volume of the cone.
Max profit when total cost and selling cost are given
The total cost of producing a blanket per day is pounds and for this production level each blanket may be sold for pounds. How many blankets should be produced per day to maximize the total profit?
Related rate problem of a conical heap
Wheat runs from a hole in a silo at a constant rate and forms a conical heap whose base radius is treble it’s height After 1 minute the height of the heap is 20 cm. Find the rate at which … Continue reading
IB HL Integral with substitution
Let . Show that
IB Math Vertical Tangent to the folium of Descartes
The folium of Descartes is a curve defined by the equation , as shown in the following diagram. Determine the exact coordinates of the point P on the curve where the tangent is parallel to the y axis.
How to find rate of change of angle when speed is given ?
A camera at point C is 3 m from the edge of a straight section of road as shown in the following diagram. The camera detects a car traveling along the road at t=0. It then rotates, always pointing at … Continue reading
Sumant's 1 page of Math 